I was in the exact same case as you the first time around - living in a city, using public transit, not owning a car. Well, I lived in an elevator building but our apartment was 400 sq ft so storage was an issue for us with any baby gear. I used to be really condescending toward all the stroller moms in the city, wondering why they didn't just carry the baby instead. I also read the advice/opinion of tons of moms on this site who said that they never bought a stroller and didn't see any need for one. So DH and I chose a nice woven wrap and decided to not purchase a stroller until we actually saw a need for one.
Well, baby was born and the baby carrying plan worked out ok at first... except that I found it uncomfortably hot to wear her in warmer weather (she was born in August) - we became a mommy-daughter sweat factory...
Then she started gaining weight, FAST. She was easily 15 pounds by 2 months old. And, while I was healing well from the birth, I found that long walks while carrying an increasingly heavier baby put a big strain on things "down there". I could go long distances if I wasn't carrying anything, but could only walk about 15 blocks comfortably if I was carrying the baby and her gear. (This kept up till she was about 5 months old, btw...)
Oh, speaking of the gear -- I promise, I'm a minimalist about these things (for example, I exclusively breastfed so I never had to carry around a bottle or pump or anything), but still, at the very least, I needed a bag to carry a changing pad, diapers, wipes, spitup cloth, and change of clothes. And my wallet, cell phone, keys, whatever. The thing that worked for us was to use a backpack. Not an elegant-looking solution at all, but it kept me hands free which was important.
There's also the question of where you'll put the stuff you acquire while you're out with baby. Groceries, library books, other shopping... I used the backpack for this, and my shopping was really limited to whatever would fit inside that bag.
Long story short -- I found it limiting to get around the city by myself with the baby in a wrap. When out with DH, it was a whole different story. He could carry the baby, and I could carry the backpack, and we could zip around having a great time. I just felt excessively burdened by the weight and the sheer juggle of doing it all with baby in the carrier when I was out alone.
So, when she was 3 months old I got a stroller. I chose the Bumbleride Flite because it folded up small enough to fit in the closet, it didn't weigh too much, and it had a deep recline with a footrest. The recline is honestly deep enough that I would have felt comfortable putting her in it at 6 weeks (it also came with a removable head support thing). But you can also buy a bassinet or a car seat in the stroller if you choose to purchase those accessories. I also got a diaper bag (Skip Hop brand) that clipped onto the frame of the stroller. Specifically, it can clip on down low instead of right up where your hands grip the stroller, which means that tipping was never an issue. This left the (tiny) storage basket under the stroller free for other things.
Things I discovered once I got the stroller (both good and bad):
I could change her diaper anywhere! Just recline the stroller and stick a changing pad under her. This freed me up from worrying about finding public restrooms with changing tables. Well, except for wintertime when the weather is extremely cold and you don't want to change baby outdoors.
We went for more walks. I got out of the house more.
The stroller limited the stores I could go into (because so many stores have narrow aisles).
It was much easier to keep baby warm in winter by wearing her.
It's a pain to carry a stroller up/down stairs (many subways in our city didn't have elevators).
It's a major pain to fold the stroller to ride the bus when the baby is not yet able to sit or stand independently. You really need a stroller that folds with one hand so that you can hold the baby, but most strollers with this feature do not fold compactly, and when they are folded they only want to lay down flat (i.e. in the trunk of a car) - they do not stand up by themselves.
She loved napping in the stroller. This was a huge deal as she grew bigger and stopped enjoying naps in the carrier. Having a place for baby to nap comfortably is essential for longer outings.
When she was around 7 months we got a jogging stroller, and it was true heaven. (We got a Joovy Zoom 360 - love it love it love it.) I couldn't take it on public transport, but I could push it easily one handed and we could go for miles in that thing. The storage basket underneath is gigantic so I could do tons of grocery shopping. The jogger also has a deep recline and a great sun canopy so it proved great for stroller naps. My daughter LOVED stroller naps. Oh, the jogger also came with an awesome rain shield, which was very useful for yucky weather outings. (The rain shield on our umbrella stroller is useless.)
In closing (what a ramble this is!...):
While I encourage a "wait and see" approach to the purchase of ANY piece of baby gear, I do now understand the importance of a good stroller for car-free families living in cities. You are right to consider the fact that you live in a 3rd floor walkup... Is there any possibility of storage on the entry level? A storage room, or an unused area under a stairway, or by the front door? Perhaps you could ask neighbors whether they mind if you stored the stroller in some out of the way area at the entrance. There would be some security risk, but probably only minimal. I'd discourage you from storing the stroller outside. The rain and snow and sun will make it a wreck (I've seen this happen so many times!) - if you keep the stroller in decent shape you can probably sell it on craig's list or something when you're through with it.
Edited by LightForest - 8/29/12 at 12:19pm